Yes, that is all such good advice. I don't think it's offensive at all to offer the book! I gave one of mine to a new mom/client who was struggling, and I just offered it up with something like "This book saved my sanity, and gave me such a happy baby..." I'd even highlight the sections that are important to her situation! I think that is so caring. LOVING the sign idea!!!!
It's so funny, isn't it, that once you've been through those first exhausting weeks with your own lo, you just want to help every new mom???
Hugs to your SIL.....if I may suggest, be "that person" for her, the one who says quietly when you're alone with her "I know this is so so hard and the feelings are overwhelming and you might even be feeling mixed up. EVERY new mom feels those feelings, but nobody talks about it. I understand, and I'm here to listen/help/hold your hand....whatever."